Abstract: I describe two new directions for composite Higgs models, both of which can reduce the tuning needed to obtain a 125 GeV Higgs. The first approach has a tree-level quartic whose size can be adjusted without tuning. This happens in 6 dimensional warped models, which can also be nicely described in terms of a deconstructed 5D theory. The second direction is to explore models where the G/H coset space is symmetric, which allows the presence of a Higgs parity operator and a simple general parameterization of the low energy effective theory in terms of a linear representation of the Goldstone fields. We observe that the case with an enhanced global symmetry (maximal symmetry) generically leads to a finite Higgs potential and a reduction in the tuning from the case of the generic composite Higgs models.